SOLUTION: A triangle has two sides of length 1 and 13. What is the largest possible whole-number length for the third side

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Question 1191537: A triangle has two sides of length 1 and 13. What is the largest possible whole-number length for the third side

Found 3 solutions by josgarithmetic, ikleyn, math_tutor2020:
Answer by josgarithmetic(39617) About Me  (Show Source):
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unknown triangle side length x

Sum of any two sides must be larger than the other side.
system%281%2B13%3Ex%2Cx%2B1%3E13%2Cx%2B13%3E1%29

system%28x%3C14%2Cx%3E12%2Cx%3E-12%29
Last inequality not useful.

system%28x%3C14%2Cx%3E12%29
The whole value between these two is 13.

system%28cross%28x%3E14%29%2Ccross%28x%3C12%29%2Ccross%28x%3C-12%29%29
Largest whole number, 11.

Answer by ikleyn(52778) About Me  (Show Source):
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.
A triangle has two sides of length 1 and 13. What is the largest possible whole-number length for the third side
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The correct answer is  13.

The answer  11,  given by @josgarithmetic,  is  INCORRECT.



Answer by math_tutor2020(3816) About Me  (Show Source):
You can put this solution on YOUR website!

a = 1 and b = 13 are the known sides of the triangle.
c is the missing side.

Due to the modified version of the triangle inequality theorem, we could say,
b-a < c < b+a
13-1 < c < 13+1
12 < c < 14

If c is restricted to whole numbers only, then c = 13 is the only possibility.

Answer: 13